The formula for calculating the inductance of the spiral in MWO

Hello all,

I want to implement a spiral inductor of 6.08 nH using spiral inductor in Micro Wave Office. Is there any formula for calculating the inductance of the spiral ?

Thanks in advance

MWO has an option to measure the inductance of an inductor (series or parallel connection).

The calculations in
S. S. Mohan, et al., “Simple Accurate Expressions for Planar Spiral Inductances”, IEEE JSSC, vol. 34, pp. 1419-1424, Oct. 1999
are widely used.

On line calculator using these equations:
http://smirc.stanford.edu/spiralCalc.html

From my experience, the equations are pretty accurate.

Thank you both of you. Could please tell in detail what option is available in MWO for calculating the inductance.

Secondly, I am using the calculator for determining the inductance, but when I am placing it instead of my inductor it does not work. The performance is deteriorated. Is it because the spiral has some resistive and capacitive effects too. What can I use instead of planar spiral for get inductance?

Thanks in advance

PS:
Further, when I am verifying the inductance of my design (determined using the above calculator) and function L_SRL in MWO. The values appear to be -ve. Am I choosing the right inductor MCINDN (Circular Microstrip Inductor without bridge). I have also tried the square spiral still - ve values.

Very confused..

Thanks in advance.

The shunt capacitance to ground below can be an issue. If you are working on PCB, maybe you can take away the ground below the inductor?

I developed a small program starting from these formulas (only for the monomial fit). Results seem interesting, but I am a bit worried about their application on a real circuit.
Indeed they don't seem to take into account a ground plane, so I suppose they are only valid if there is no ground plane below.
Another question: are these formulas also valid for 1-turn inductors? I need to design a very small inductor, and according to the formulas I am unable to use a 2- or 3- turns model.

P.S.: I am referring to the PCB inductor formulas that volker_muehlhaus cites

The textbook equations are valid only if you have NO ground below. They are still ok for inductors over most silicon substrates, but with a good conductor below (PCB with back side metalization) you will get very different results.

Regarding the 1 turn inductor: the equations are based on some average diameter calculation, and work fine for single turn inductors.

Thank you for your answer.
I suppose one is restricted to either current sheet or modified Wheeler for 1-turn inductors. I will change the software consequently.